The man in Fig. weighs 180 lb; the platform and attached frictionless pulley weigh a total of 43 lb. Ignore theweight of the rope. With what force must the man pull up on the rope in order to lift himself and the platform upward at 1.2 ft/s2?

The combined weight of the system is the sum of the weight of the man and the weight of the platform, that is
W2 = W1 +weight of platform

Therefore, the combined weight of the man-platform system is 223 lb.
The combined mass of the man-platform system is,

Here g is the magnitude of acceleration due to gravity.

Therefore the combined mass of the man-platform system is 100.9 kg.

Therefore, the force exerted by the man to lift the platform is 1,027 N .